An Equation-Solving Solution Gradient Strategy for High-Resolution and Compact Discretization of Hyperbolic Conservation Laws

Abstract

The present study extends our previous formulation in simulating steady incompressible Navier-Stokes equations to solving unsteady compressible flows. It is designed by taking the solution gradient as an additional computational variable to build a high-resolution and compact discretization. Essential ingredients concerning the derivation procedure are detailed in the frame of general hyperbolic conservation laws. Numerical analyses on modeled problems are performed to reveal its stability criterion and formal accuracy. Several one- and two-dimensional problems are solved numerically, and the computational results are compared with those acquired by existing schemes to demonstrate their relative efficiency. It is found that the present formulation will be a useful tool to simulate general hyperbolic conservation laws.